Phase Retrieval using Nonlinear Curvature Sensing within Convergent Beams

Abstract: Path-length diversity methods may be used for adaptive optics (AO) systems to retrieve phase and amplitude information by measuring intensity across multiple planes. Observations that rely on free-space propagation, such as the nonlinear curvature wavefront sensor (WFS), have been shown to offer excellent sensitivity and robustness to scintillation. However, the default design results in a large opto-mechanical footprint due to unavoidable geometric-optics and wave-optics effects. Measurements recorded in a convergent beam would improve instrument compactness, while concentrating light into smaller detector regions of interest, improving signal-to-noise ratio and possibly wavefront reconstruction speed. In this paper, we study path-length diversity wavefront sensing using four planes of contemporaneous intensity measurements made in a convergent beam. We develop a physical optics propagation model and validate the model by performing wavefront reconstructions in both simulations and lab experiments. The manuscripts core contribution is a practical, intensity-domain, Fourier-transform-based recipe to use a conventional multi-plane Gerchberg-Saxton (or comparable) reconstruction pipeline with convergent-beam measurements, enabling a compact optical layout. We find that this approach offers practical benefits over an equivalent free-space wavefront sensor, in particular reducing size, weight, complexity and cost.